SOLUTION: A certain number leaves a remainder of 4 when divided by 5, a remainder of 5 when divided by 6, and a remainder of 6 when divided by 7. Find the smallest number that satisfies thes

Question 1016489: A certain number leaves a remainder of 4 when divided by 5, a remainder of 5 when divided by 6, and a remainder of 6 when divided by 7. Find the smallest number that satisfies these conditions.
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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A certain number leaves a remainder of 4 when divided by 5, a remainder of 5 when divided by 6, and a remainder of 6 when divided by 7. Find the smallest number that satisfies these conditions.
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Let n be your number.

Add 1 (one) to n.

Then n+1 is multiple of 5, of 6 and of 7.

The smallest integer positive n+1 with such properties is 5*6*7 = 210.

Hence your number n is 210 - 1 = 209.

See the lesson The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9 in this site.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A certain number leaves a remainder of 4 when divided by 5,
The number has to end in a 4 or a 9
:
a remainder of 5 when divided by 6, and
multiples of 6 +5 ending in 4 or 9
29, 59, 89, 119, 149, 179, 209, 239, 269
:
a remainder of 6 when divided by 7.
multiples of 7 + 6 ending in 9 (4 does not appear in the previous list)
69, 139, 209, 279
:
Find the smallest number that satisfies these conditions.
looks like 209 is the winner!
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